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Petrov classification information


In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold.

It is most often applied in studying exact solutions of Einstein's field equations, but strictly speaking the classification is a theorem in pure mathematics applying to any Lorentzian manifold, independent of any physical interpretation. The classification was found in 1954 by A. Z. Petrov and independently by Felix Pirani in 1957.

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Petrov classification

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geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries...

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Aleksei Zinovyevich Petrov

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noted for his work on the classification of Einstein spaces, today called Petrov classification. The Petrov classification is related with the Weyl tensor...

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Classification theorem

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components Ratner classification theorem Classification of electromagnetic fields Petrov classification – Classification used in differential geometry and general...

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Exact solutions in general relativity

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often stated in terms of the Petrov classification of the possible symmetries of the Weyl tensor, or the Segre classification of the possible symmetries...

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Weyl tensor

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expression for the Weyl tensor. Lanczos tensor Peeling theorem Petrov classification Plebanski tensor Weyl curvature hypothesis Weyl scalar Weyl, Hermann...

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Mathematics of general relativity

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tensor classifications useful in general relativity include the Segre classification of the energy–momentum tensor and the Petrov classification of the...

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Speed of gravity

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not a gravitomagnetic component (gravitational radiation); see Petrov classification. The gravitoelectric field is a static field and therefore cannot...

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Felix Pirani

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classification of the Weyl tensor, which he discovered in 1957 independently of A.Z. Petrov and is sometimes called the Petrov-Pirani classification....

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Segre classification

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application in the classification of exact solutions in general relativity. Corrado Segre Jordan normal form Petrov classification Stephani, Hans; Kramer...

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Spacetime symmetries

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spacetimes, including using the Segre classification of the energy–momentum tensor or the Petrov classification of the Weyl tensor have been studied extensively...

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Plebanski tensor

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symmetries of the Plebanski tensor in a manner analogous to the Petrov classification. Plebański, J. (1964), "The Algebraic structure of the Tensor of...

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Peeling theorem

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Weyl tensor, and abstract index notation is used. Moreover, in the Petrov classification, C a b c d ( 1 ) {\displaystyle C_{abcd}^{(1)}} is type N, C a b...

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Classification of electromagnetic fields

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Electromagnetic peeling theorem Electrovacuum solution Lorentz group Petrov classification The rank given here corresponds to that as a linear operator or...

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John Lighton Synge

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the Dublin Institute for Advanced Studies 14, Series A) 1964 The Petrov Classification of Gravitational Fields; Pub: DIAS (Communications of the Dublin...

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Timeline of gravitational physics and relativity

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diagrams and geometrical methods. 1957 – Felix A. E. Pirani uses Petrov classification to understand gravitational radiation. 1957 – Richard Feynman introduces...

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List of contributors to general relativity

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hypothesis, highly influential monograph), Alexei Zinovievich Petrov (Petrov classification of algebraic properties of Weyl curvature tensor), Tsvi Piran...

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GRTensorII

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efficient computation of Ricci and Weyl spinor components and of Petrov classification efficient computation of the Carminati-McLenaghan invariants and...

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Ricci decomposition

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flat. Bel decomposition of the Riemann tensor Conformal geometry Petrov classification Plebanski tensor Ricci calculus Schouten tensor Trace-free Ricci...

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Construction of a complex null tetrad

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Demystified - A Self-Teaching Guide. Chapter 9: Null Tetrads and the Petrov Classification. New York: McGraw-Hill, 2006. Subrahmanyan Chandrasekhar. The Mathematical...

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Unified Sports Classification System of the USSR and Russia

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Unified Sports Classification System of the USSR (Russian: Единая Всесоюзная спортивная классификация) is a document which provided general Soviet physical...

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Vivianite

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that it is particularly associated with gossan, but this is disputed by Petrov. Associated minerals include metavivianite, ludlamite, pyrite, siderite...

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Partial differential equation

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such knowledge is more specialized. The elliptic/parabolic/hyperbolic classification provides a guide to appropriate initial and boundary conditions and...

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Georgi Petrov Georgiev

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Mountains classification 10th Overall Tour of Mersin "Georgi Petrov Georgiev". ProCyclingStats. Retrieved 16 August 2016. Georgi Georgiev Petrov at UCI Georgi...

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